Knowledge Bank

An alternative specification of rotating body-fixed axes reduces the relevant group of covering operations from $Dooh$ to $D4h$ for linear molecules having a center of symmetry and from $Coov$ to $C4v$ for others. Simple Justification can be given for transformation of Wilson-Howard rotation-vibration Hamiltonian into Darling-Dennison form. An alternative to the Watson result,\frac{1}{2}\mu^{1/4}\Sigma_{k}P_{k}\mu^{-1/2}P_{k}\mu^{1/4}=\frac{1}{2}\Sigma_{k}P^{2}_{k}+\mbox{Watson term”,} can be given which reduces to his form for nonlinear molecules but which reduces the Watson term” to zero for linear molecules with the aid of the Anat-Henry specification of rotary inertia coefficients in the Hamiltonian, As a result, the classical and quantum-mechanical forms of the rotation-vibration Hamiltonian of a linear molecule are identical in appearance.